Related papers: Practical non-Abelian Stokes theorem for topologic…
It is shown that the application of the non-Abelian Stokes theorem to the computation of the operators constructed with Wilson loop will lead to ambiguity, if the gauge field under consideration is a non-trivial one. This point is…
The non-Abelian Stokes theorem for loop variables associated with nontrivial loops (knots and links) is derived. It is shown that a loop variable is in general different from unity even if the field strength vanishes everywhere on the…
In this short review main issues related to the non-Abelian Stokes theorem have been addressed. The two principal approaches to the non-Abelian Stokes theorem, operator and two variants (coherent-state and holomorphic) of the path-integral…
A formula constituting the non-Abelian Stokes theorem for general semi-simple compact gauge groups is presented. The formula involves a path integral over a group space and is applicable to Wilson loop variables irrespective of the topology…
We present the non-Abelian Stokes theorem for the Wilson loop in various forms and discuss its meaning. Its validity has been recently questioned by Faber, Ivanov, Troitskaya and Zach. We demonstrate that all points of their criticism are…
We derive a new non-abelian Stokes theorem by rewriting the Wilson loop as a gauge-invariant area integral, at the price of integrating over an auxiliary field from the coset SU(N) / [U(1)]^{N-1} space. We then introduce the relativistic…
We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes' theorem.
We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as…
We discuss the non-Abelian Stokes theorem for SU(2) gauge fields which avoids both additional integration variables and surface ordering. The idea is to introduce the instant color orientation of the flux piercing the loop. The non-Abelian…
Using product integrals we review the unambiguous mathematical representation of Wilson line and Wilson loop operators, including their behavior under gauge transformations and the non-abelian Stokes theorem. Interesting consistency…
A simple analytic proof of the formula known as the non-Abelian Stokes theorem is given. It is explicitly shown that the consistency of the formula is guaranteed by the Bianchi identity for the gauge field. An attempt is made to construct…
We derive the Abelian - like expression for the lattice SU(N) Wilson loop in arbitrary irreducible representation. The continuum Abelian representation of the SU(N) Wilson loop (for the loop without selfintersections) that has been obtained…
We introduce an approach to expand gauge-invariant Wilson operators on lattice. This approach is based on non-abelian Stokes theorem and overcomes some shortage of some former methods. It is also suitable for expanding any Wilson operators…
The paper is a chapter of the above-mentioned book. It aims to give an expository presentation of author's version of the non-Abelian Stokes theorem in the framework of path-integral formalism.
We derive a version of non-Abelian Stokes theorem for SU(2) gauge fields in which neither additional integration nor surface ordering are required. The path ordering is eliminated by introducing the instantaneous color orientation of the…
We generalize the standard product integral formalism to incorporate Grassmann valued matrices and show that the resulting supersymmetric product integrals provide a natural framework for describing supersymmetric Wilson Lines and Wilson…
We derive a generalized Stokes' theorem, valid in any dimension and for arbitrary loops, even if self intersecting or knotted. The generalized theorem does not involve an auxiliary surface, but inherits a higher rank gauge symmetry from the…
We give a gauge-independent definition of magnetic monopoles in the $SU(N)$ Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for…
An open problem in theory of loops is to find the variety of non- Moufang loops satisfying the Moufang Theorem. In this note, we present a variety of local smooth diassociative loops with such property.
Foundational cases of the generalized Stokes' theorem are visualized using geometric algebra. From considering bivector valued fields, two seldom used instances of the theorem are obtained. Graphical representations are given, showing a…